Sometimes coadjoint orbits are studied in the infinite-dimensional case (for example in study of Virasoro algebra).

Properties

As symplectic leafs of the Lie-Poisson structure

The dual $g^*$ of a (say finite-dimensional real) Lie algebra has a structure of a Poisson manifold with the Poisson structure due to A. Kirillov and Souriau, called the Lie-Poisson structure, namely for any $a\in g^*$,

B. C., The Structure of the Space of Coadjoint Orbits of an Exponential Solvable Lie Group, ransactions of the American Mathematical Society Vol. 332, No. 1 (Jul., 1992), pp. 241-269, (JSTOR)

Revised on October 29, 2013 23:46:24
by Urs Schreiber
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